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Provides overall picture of source populations Compare with models for populations and their evolution populations of black-holes and neutron stars in galaxies, populations of stars in star-custers, distribution of dark matter in the universe Provides picture of their evolution in the Universe Importance of LogN-LogS distributions

6
Start with an image How we do it CDF-N Alexander etal 2006; Bauer etal 2006

13
Statistical issues Source significance : what is the probability that my source is a background fluctuation ? Intensity uncertainty : what is the real intensity (and its uncertainty) of my source given the background and instrumental effects ? Position uncertainty : what is the probability that my source is the same as another source detected 3 pixels away in a different exposure ? what is the probability that my source is associated with sources seen in different bands (e.g. optical, radio) ? Completeness (and other biases) : How many sources are missing from my set ? Detection

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If we assume a source dependent flux conversion The above formulation can be written in terms of S and  Poisson errors, Poisson source intensity, incompleteness (Zezas etal 1997) Number of sources with m observed counts Likelihood for total sample (treat each source as independent sample) Fitting methods (extension SM 86)